Seeking Your Advice on My Course Planning

[bacte2013]

Dear Physics Forum advisers,

I am a rising college junior in U.S. with a major in mathematics, and an aspiring applied mathematician. I apologize for this sudden interruption, but I wrote this email to seek your advice on my current problem on the course selection. I will very soon be conducting an undergraduate research on the complexity theory (abstract, math-heavy) and the computer security (mixed math and programming).

I am currently registered for the Multivariable Calculus, Linear Algebra with Introduction to Proofs, College Geometry, and Undegraduate Research. my research advisers want me to take the Abstract Algebra I instead of College Geometry since my research topics heavily uses the algebra. Although the Abstract Algebra I has a prerequisite of Linear Algebra (one I registered), the professor for that course said he will give me an enrollment position if I think I am ready for that course. After the end of Spring Semester, I read through the "Mathematical Proofs" by Gary Chartrand and acquired the basic proof skills. Currently, I am studying Artin's Algebra, Hoffman/Kunze's Linear Algebra, and Lang's Calculus of Several Variables, which all are very fascinating books. My linear algebra course will use Friedberg/Insel/Spence and my abstract algebra I course will use Dummit/Foote. I am not sure if it is safe for me to take the linear algebra with abstract algebra all together. Multivariable calculus will not be a major problem since it is a computational level (using a course packet at the level of Lang). What should I do? Could you suggest the possible guidelines to decide whether I should take both LA and AA together?PK

 

[Student100]

Listen to your research adviser, taking both shouldn't be a problem if you feel comfortable with logic. Typically, linear is only a prerequisite to ensure you have some kind of experience with proofs.

 

[bacte2013]

I see. Is it safe for me to not having a comprehensive understanding on the linear algebra before the abstract algebra? I have been rigorously building my reasoning skill, but I am still in Chapter 3 of Hoffman/Kunze.

 

[Student100]

I see. Is it safe for me to not having a comprehensive understanding on the linear algebra before the abstract algebra? I have been rigorously building my reasoning skill, but I am still in Chapter 3 of Hoffman/Kunze.

You should be okay as long as proofs don't scare you and you personally feel comfortable with the idea. I don't think your research adviser would recommend it if he did't feel you were capable of doing it, so I'm basing all this on his recommendation. There are some mathematical structures in LA you will encounter in AA, but it may be interesting from a conceptual standpoint to actually study abstract algebra while doing linear. Again, it's mostly a prerequisite to ensure you aren't going to hit the door running and give up on math when switching from the calculation based lower maths to the more logic heavy upper division courses.